Ordinary Differential Equations in the Complex Domain (Dover Books on Mathematics) by Einar Hille (PDF)

Description

Graduate-level text offers full treatments of existence theorems, representation of solutions by series, theory of majorants, dominants and minorants, questions of growth, much more. Includes 675 exercises. Bibliography.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I bought this because I enjoyed.Analytic Function Theory. I haven’t finished reading it, but it covers a lot of ground and is pretty readable. (warning: I have a phd in math, so readable for me might mean something different.)

⭐A remarkable work, even to this day, and very useful.

⭐very good

⭐It arranged many papers about complex domain O.D.E. It open the door to this topic.

⭐After an Introduction, which provides the necessary fundamental facts with didactic skill, chapters concerning Existence and Uniqueness, and Singularities follow. After the 4th chapter dealing with Riccati’s Equation the main point are linear DE of second order. The book continues with chapters on special topics (7 Representation Thms, 8 Complex Oscillation Theory, 9 Linear nth Order and Matrix DE, 10 The Schwarzian). At the end nonlinear DE are treated. The extensive field in the title is explained deeply and very lucidly yet on an elementary level. However, at some points there are difficulties (e. g. some passages where the exposition is too brief). The exercises at the end of every section, which are at least in part easy, are very instructive. The index is good and the lists of references include many original work which, however, are generally quite old. Unfortunately there is no index of symbols. Chapter 9 on Linear nth Order and Matrix DE is brilliant in my opinion.

⭐Questo è un testo unico da non farsi Assolutamente mancare in biblioteca. Molti testo si trovano sulle ODE ma nessuno che affronti le ODE nel campo complesso. Al più lo fanno solo in modo marginale. Hille invece lo fa percorrendo lo in lungo e in largo. Qui vi è un concentrato della sapienza di questo grande matematico che ha dato eccezionali contributi all’analisi (solo un es., il teore di Hille-Yosida). Fantastico in tutti i sensi.

⭐

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